diff -r 8268b277d240 -r e73bd379e839 Nominal/nominal_induct.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Nominal/nominal_induct.ML Thu Dec 30 10:00:09 2010 +0000 @@ -0,0 +1,185 @@ +(* Author: Christian Urban and Makarius + +The nominal induct proof method. +*) + +structure NominalInduct: +sig + val nominal_induct_tac: Proof.context -> bool -> (binding option * (term * bool)) option list list -> + (string * typ) list -> (string * typ) list list -> thm list -> thm list -> int -> Rule_Cases.cases_tactic + + val nominal_induct_method: (Proof.context -> Proof.method) context_parser +end = + +struct + +(* proper tuples -- nested left *) + +fun tupleT Ts = HOLogic.unitT |> fold (fn T => fn U => HOLogic.mk_prodT (U, T)) Ts; +fun tuple ts = HOLogic.unit |> fold (fn t => fn u => HOLogic.mk_prod (u, t)) ts; + +fun tuple_fun Ts (xi, T) = + Library.funpow (length Ts) HOLogic.mk_split + (Var (xi, (HOLogic.unitT :: Ts) ---> Term.range_type T)); + +val split_all_tuples = + Simplifier.full_simplify (HOL_basic_ss addsimps + @{thms split_conv split_paired_all unit_all_eq1}) +(* + @{thm fresh_unit_elim}, @{thm fresh_prod_elim}] @ + @{thms fresh_star_unit_elim} @ @{thms fresh_star_prod_elim}) +*) + + +(* prepare rule *) + +fun inst_mutual_rule ctxt insts avoiding rules = + let + val (nconcls, joined_rule) = Rule_Cases.strict_mutual_rule ctxt rules; + val concls = Logic.dest_conjunctions (Thm.concl_of joined_rule); + val (cases, consumes) = Rule_Cases.get joined_rule; + + val l = length rules; + val _ = + if length insts = l then () + else error ("Bad number of instantiations for " ^ string_of_int l ^ " rules"); + + fun subst inst concl = + let + val vars = Induct.vars_of concl; + val m = length vars and n = length inst; + val _ = if m >= n + 2 then () else error "Too few variables in conclusion of rule"; + val P :: x :: ys = vars; + val zs = drop (m - n - 2) ys; + in + (P, tuple_fun (map #2 avoiding) (Term.dest_Var P)) :: + (x, tuple (map Free avoiding)) :: + map_filter (fn (z, SOME t) => SOME (z, t) | _ => NONE) (zs ~~ inst) + end; + val substs = + map2 subst insts concls |> flat |> distinct (op =) + |> map (pairself (Thm.cterm_of (ProofContext.theory_of ctxt))); + in + (((cases, nconcls), consumes), Drule.cterm_instantiate substs joined_rule) + end; + +fun rename_params_rule internal xs rule = + let + val tune = + if internal then Name.internal + else fn x => the_default x (try Name.dest_internal x); + val n = length xs; + fun rename prem = + let + val ps = Logic.strip_params prem; + val p = length ps; + val ys = + if p < n then [] + else map (tune o #1) (take (p - n) ps) @ xs; + in Logic.list_rename_params (ys, prem) end; + fun rename_prems prop = + let val (As, C) = Logic.strip_horn prop + in Logic.list_implies (map rename As, C) end; + in Thm.equal_elim (Thm.reflexive (Drule.cterm_fun rename_prems (Thm.cprop_of rule))) rule end; + + +(* nominal_induct_tac *) + +fun nominal_induct_tac ctxt simp def_insts avoiding fixings rules facts = + let + val thy = ProofContext.theory_of ctxt; + val cert = Thm.cterm_of thy; + + val ((insts, defs), defs_ctxt) = fold_map Induct.add_defs def_insts ctxt |>> split_list; + val atomized_defs = map (map (Conv.fconv_rule Induct.atomize_cterm)) defs; + + val finish_rule = + split_all_tuples + #> rename_params_rule true + (map (Name.clean o ProofContext.revert_skolem defs_ctxt o fst) avoiding); + + fun rule_cases ctxt r = + let val r' = if simp then Induct.simplified_rule ctxt r else r + in Rule_Cases.make_nested (Thm.prop_of r') (Induct.rulified_term r') end; + in + (fn i => fn st => + rules + |> inst_mutual_rule ctxt insts avoiding + |> Rule_Cases.consume (flat defs) facts + |> Seq.maps (fn (((cases, concls), (more_consumes, more_facts)), rule) => + (PRECISE_CONJUNCTS (length concls) (ALLGOALS (fn j => + (CONJUNCTS (ALLGOALS + let + val adefs = nth_list atomized_defs (j - 1); + val frees = fold (Term.add_frees o prop_of) adefs []; + val xs = nth_list fixings (j - 1); + val k = nth concls (j - 1) + more_consumes + in + Method.insert_tac (more_facts @ adefs) THEN' + (if simp then + Induct.rotate_tac k (length adefs) THEN' + Induct.fix_tac defs_ctxt k + (List.partition (member op = frees) xs |> op @) + else + Induct.fix_tac defs_ctxt k xs) + end) + THEN' Induct.inner_atomize_tac) j)) + THEN' Induct.atomize_tac) i st |> Seq.maps (fn st' => + Induct.guess_instance ctxt + (finish_rule (Induct.internalize more_consumes rule)) i st' + |> Seq.maps (fn rule' => + CASES (rule_cases ctxt rule' cases) + (Tactic.rtac (rename_params_rule false [] rule') i THEN + PRIMITIVE (singleton (ProofContext.export defs_ctxt ctxt))) st')))) + THEN_ALL_NEW_CASES + ((if simp then Induct.simplify_tac ctxt THEN' (TRY o Induct.trivial_tac) + else K all_tac) + THEN_ALL_NEW Induct.rulify_tac) + end; + + +(* concrete syntax *) + +local + +val avoidingN = "avoiding"; +val fixingN = "arbitrary"; (* to be consistent with induct; hopefully this changes again *) +val ruleN = "rule"; + +val inst = Scan.lift (Args.$$$ "_") >> K NONE || + Args.term >> (SOME o rpair false) || + Scan.lift (Args.$$$ "(") |-- (Args.term >> (SOME o rpair true)) --| + Scan.lift (Args.$$$ ")"); + +val def_inst = + ((Scan.lift (Args.binding --| (Args.$$$ "\" || Args.$$$ "==")) >> SOME) + -- (Args.term >> rpair false)) >> SOME || + inst >> Option.map (pair NONE); + +val free = Args.context -- Args.term >> (fn (_, Free v) => v | (ctxt, t) => + error ("Bad free variable: " ^ Syntax.string_of_term ctxt t)); + +fun unless_more_args scan = Scan.unless (Scan.lift + ((Args.$$$ avoidingN || Args.$$$ fixingN || Args.$$$ ruleN) -- Args.colon)) scan; + + +val avoiding = Scan.optional (Scan.lift (Args.$$$ avoidingN -- Args.colon) |-- + Scan.repeat (unless_more_args free)) []; + +val fixing = Scan.optional (Scan.lift (Args.$$$ fixingN -- Args.colon) |-- + Parse.and_list' (Scan.repeat (unless_more_args free))) []; + +val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.colon) |-- Attrib.thms; + +in + +val nominal_induct_method = + Args.mode Induct.no_simpN -- (Parse.and_list' (Scan.repeat (unless_more_args def_inst)) -- + avoiding -- fixing -- rule_spec) >> + (fn (no_simp, (((x, y), z), w)) => fn ctxt => + RAW_METHOD_CASES (fn facts => + HEADGOAL (nominal_induct_tac ctxt (not no_simp) x y z w facts))); + +end + +end;